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Something very vital to keep in mind is that the best performers are not necessarily the best teachers.

... And the best teachers are not necessarily the best performers.

For a more serious post than my last, I agree with both of you. Performing and teaching are entirely different skill sets, and proficiency in one does not necessarily translate to proficiency in the other.

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Every day we are afforded a new chance. The problem with life is not that you run out of chances. In the end, what you run out of are days.

I would be quite curious to know how one classifies a piano teacher as 'the best piano teacher in the world/US/whatever'.

I mean what are the criteria? Is it for which students come out of them? So the teacher who produces the best soloists or the pianists with the more prominent career? Is it the one who provides excellent fundamentals of music? One who can offer a degree? One who is REALLY REALLY REALLY beautiful? etc...

One problem is that there are literally dozens of teachers who have excellent reputations and do amazing work with their students.

As has already been said, it matters a great deal what you're looking for in a teacher. What character and combination of technical, musical, and career advice do you want? Is the "name" of the teacher/institution important to you? What kind of career do you want beyond school? What kind of repertoire interests you? How important is geographic location?

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"If we continually try to force a child to do what he is afraid to do, he will become more timid, and will use his brains and energy, not to explore the unknown, but to find ways to avoid the pressures we put on him." (John Holt)

Or a teacher that provides excellent fundamentals and instills a passion for music in her young students. Most of her students keep playing through adulthood. And some of her students have had career successes in jazz, composition and rock, but her students who have pursued careers in classical music haven't reached that same pinnacle (yet). I'll bet you have never heard of her (and are likely not to know her name ever). Still, a great teacher.